Faraday’s law of electromagnetic induction states that the magnitude of the induced emf ε is equal to the time rate of magnetic flux through the circuit. Let ∆Ф is the change in the magnetic flux during time interval ∆t, then the mathematical form of the law is
Now let the coil consists of N turns and carrying a current I. The emf ε in the coil will be given by
Since the current flows in all the turns of the coil, therefore, the flux linkages due to N turns of the coil is proportional to the current I in the coil.
This proves the statement.